The Nationals are getting right-handed pitcher Mason Thompson and shortstop Jordy Barley in return. Both are in the minors.
Hudson is currently on the COVID-19 injured list. He's 4-1 with a 2.20 ERA in 31 appearances this season.
He was activated earlier this month from the injured list after recovering from right elbow inflammation.
The 34-year-old Hudson does have a history of injuries, including two Tommy John surgeries between 2012 and 2013 while with the Arizona Diamondbacks.
He joined the Nationals in a midseason trade with the Toronto Blue Jays in 2019 and recorded the final three outs in Game 7 of the World Series a few months later.
Information from The Associated Press contributed to this report.